Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#532 | C2 | semidirect |
| 2. #90168 | C2 | semidirect |
| 3. #90010 | C2 | semidirect |
| 4. #89855 | C2 | semidirect |
| 5. #89844 | C2 | semidirect |
| 6. #89830 | C2 | semidirect |
| 7. #89827 | C2 | semidirect |
| 8. #89698 | C2 | semidirect |
| 67. #532 | D7 | semidirect |
| 210. C7 | #3214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#532 | 2 |
| #90168 | 2 |
| #90010 | 2 |
| #89855 | 2 |
| #89844 | 2 |
| #89830 | 2 |
| #89827 | 2 |
| #89698 | 2 |
| #3214 | 7 |